Abstract:We introduce n/p-harmonic maps as critical points of the energy E(v) = ∫|Δα∕2v|p where pointwise v : D ⊂ ℝn→ SN-1, for the N-sphere SN-1⊂ ℝN and α = n∕p. This energy combines the non-local behaviour of the fractional harmonic maps introduced by Riviere and first author with the degenerate arguments of the n-laplacian. In this setting, we will prove Hölder continuity.